Joint modelling of location and scale parameters of the skew-normal distribution

Abstract Skewed data are common in sample surveys. In probability proportional to size sampling, we propose two Bayesian model-based predictive methods for estimating finite population quantiles with skewed sample survey data. We assume the survey outcome to follow a skew-normal distribution given the probability of selection and model the location and scale parameters of the skew-normal distribution as functions of the probability of selection. To allow a flexible association between the survey outcome and the probability of selection, the first method models the location parameter with a penalized spline and the scale parameter with a polynomial function, while the second method models both the location and scale parameters with penalized splines. Using a fully Bayesian approach, we obtain the posterior predictive distributions of the nonsampled units in the population and thus the posterior distributions of the finite population quantiles. We show through simulations that our proposed methods are more efficient and yield shorter credible intervals with better coverage rates than the conventional weighted method in estimating finite population quantiles. We demonstrate the application of our proposed methods using data from the 2013 National Drug Abuse Treatment System Survey.

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EM algorithm using overparameterization for the multivariate skew-normal distribution

Econometrics and Statistics ◽

10.1016/j.ecosta.2021.03.003 ◽

2021 ◽

Author(s):

Toshihiro Abe ◽

Hironori Fujisawa ◽

Takayuki Kawashima ◽

Christophe Ley

Keyword(s):

Em Algorithm ◽

Normal Distribution ◽

Skew Normal Distribution ◽

Skew Normal

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Parameter estimation for univariate Skew-Normal distribution based on the modified empirical characteristic function

Communication in Statistics- Theory and Methods ◽

10.1080/03610926.2021.1883655 ◽

2021 ◽

pp. 1-12

Author(s):

Gege Hou ◽

Ancha Xu ◽

Fengjing Cai ◽

You-Gan Wang

Keyword(s):

Parameter Estimation ◽

Characteristic Function ◽

Normal Distribution ◽

Empirical Characteristic Function ◽

Skew Normal Distribution ◽

Skew Normal

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Some properties of the unified skew-normal distribution

Statistical Papers ◽

10.1007/s00362-021-01235-2 ◽

2021 ◽

Author(s):

Reinaldo B. Arellano-Valle ◽

Adelchi Azzalini

Keyword(s):

Normal Distribution ◽

Fourth Order ◽

Probability Distributions ◽

Skew Normal Distribution ◽

Present Contribution ◽

The Family ◽

Multivariate Skewness ◽

Unified Skew Normal Distribution ◽

Skewness And Kurtosis ◽

Skew Normal

AbstractFor the family of multivariate probability distributions variously denoted as unified skew-normal, closed skew-normal and other names, a number of properties are already known, but many others are not, even some basic ones. The present contribution aims at filling some of the missing gaps. Specifically, the moments up to the fourth order are obtained, and from here the expressions of the Mardia’s measures of multivariate skewness and kurtosis. Other results concern the property of log-concavity of the distribution, closure with respect to conditioning on intervals, and a possible alternative parameterization.

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Copulaesque Versions of the Skew-Normal and Skew-Student Distributions

Symmetry ◽

10.3390/sym13050815 ◽

2021 ◽

Vol 13 (5) ◽

pp. 815

Author(s):

Christopher Adcock

Keyword(s):

Distribution Function ◽

Normal Distribution ◽

Degrees Of Freedom ◽

Special Functions ◽

Normal Distribution Function ◽

Skew Normal Distribution ◽

Marginal Distributions ◽

Student’S T ◽

Normal Copula ◽

Skew Normal

A recent paper presents an extension of the skew-normal distribution which is a copula. Under this model, the standardized marginal distributions are standard normal. The copula itself depends on the familiar skewing construction based on the normal distribution function. This paper is concerned with two topics. First, the paper presents a number of extensions of the skew-normal copula. Notably these include a case in which the standardized marginal distributions are Student’s t, with different degrees of freedom allowed for each margin. In this case the skewing function need not be the distribution function for Student’s t, but can depend on certain of the special functions. Secondly, several multivariate versions of the skew-normal copula model are presented. The paper contains several illustrative examples.

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